CML Style Math Mock Tests for Grades 7-9 | K8 Math Spark
CML SAMPLE
TEST 1
NAME _________________________________ GRADE 7
PYTHAGOREAN DIVISION MEET 1 OCTOBER 15, 2024 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
Find the sum of 15 hundreds and 23 tens.
1) __________
2)
If x ◊ y = 2x + 3y and 4 ◊ b = 17, find the value of b.
2) __________
3)
On a number line, point P is at 8 and point Q is at 20. Point R is exactly halfway between P and Q. What is the coordinate of point R?
3) __________
4)
A rectangular prism has dimensions 4 inches by 6 inches by 3 inches. If it is divided into unit cubes, how many 1-inch cubes will there be?
4) __________
5)
Find the perimeter of a rectangle with length 12 cm and width 8 cm.
5) __________
6)
In the multiplication ABCD × 9 = DCBA, where A, B, C, D are different digits, find the 4-digit number ABCD.
6) __________
CML SAMPLE
TEST 2
NAME _________________________________ GRADE 7
EUCLIDEAN DIVISION MEET 2 NOVEMBER 12, 2024 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
What 4-digit palindrome has digits that multiply to 100? (A palindrome reads the same forward and backward.)
1) __________
2)
If k ÷ 34 = 23, find k in simplest form.
2) __________
3)
Maria jumped 3 ft. 7 in. on her first attempt. Her second jump was 2 ft. 9 in. farther. How far did she jump on her second attempt?
3) __________
4)
Triangle ABC has area 36 square units. If triangle DEF is similar to triangle ABC with a scale factor of 23, what is the area of triangle DEF?
4) __________
5)
Tom scored 85% on a test with 40 questions. How many questions did he answer correctly?
5) __________
6)
A path from point A to point B consists of moving only right or up on a grid. If A is at (0,0) and B is at (3,2), how many different paths are there?
6) __________
CML SAMPLE
TEST 3
NAME _________________________________ GRADE 8
EUCLIDEAN DIVISION MEET 3 DECEMBER 10, 2024 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
Compare: 42 × 156 ____ 156 × 43
a) < b) > c) =
a) < b) > c) =
1) __________
2)
If a ⊗ b = a+ba×b and a Δ b = a×ba+b, find the value of (3 ⊗ 4) Δ (2 ⊗ 5).
2) __________
3)
Lisa is 4 inches taller than being 5 feet tall. Her height is 45 of her father’s height. How tall is her father?
3) __________
4)
A store bought 50 notebooks for $75 and sold them for $2.25 each. What was the profit percentage?
4) __________
5)
If 2n × 32 × 52 = 1800, find n.
5) __________
6)
A box contains red and blue marbles in the ratio 3:4. If there are 21 red marbles, what is the probability of drawing a blue marble?
6) __________
CML SAMPLE
TEST 4
NAME _________________________________ GRADE 8
PYTHAGOREAN DIVISION MEET 4 JANUARY 14, 2025 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
If acbd = ad − bc,
find the value of 5234.
1) __________
2)
A water tank weighs 9 pounds plus 14 of its total weight. How much does the tank weigh?
2) __________
3)
The average of 6 numbers is 45. The average of 4 of those numbers is 38. Find the average of the remaining 2 numbers.
3) __________
4)
A circle is inscribed in a square with side length 10. A smaller square is inscribed in the circle. Find the area of the smaller square.
4) __________
5)
Simplify: 36 × 9227. Express your answer as a power of 3.
5) __________
6)
The probability of rain on Monday is p. The probability of rain on Tuesday is q. What is the probability that it rains on exactly one of these two days?
6) __________
CML SAMPLE
TEST 5
NAME _________________________________ GRADE 9
EUCLIDEAN DIVISION MEET 1 OCTOBER 8, 2024 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
The harmonic mean of x and y is 21x+1y. Find the harmonic mean of 4 and 12.
1) __________
2)
Two numbers are relatively prime if their greatest common divisor is 1. Which pair is relatively prime to 42?
a) 15 & 21 b) 28 & 35 c) 33 & 55 d) 25 & 49
a) 15 & 21 b) 28 & 35 c) 33 & 55 d) 25 & 49
2) __________
3)
A car travels 240 miles averaging 40 mph for the first part and 60 mph for the rest. If the trip took 5 hours total, how many miles were traveled at 40 mph?
3) __________
4)
The sum of n consecutive integers starting from 1 is 78. Find n.
4) __________
5)
The probability that it rains tomorrow is x. The probability it doesn’t rain is y. Find x2 + 2xy + y2.
5) __________
6)
A printer prints a repeating pattern: MATHCOUNTS… What is the 100th character?
6) __________
CML SAMPLE
TEST 6
NAME _________________________________ GRADE 9
PYTHAGOREAN DIVISION MEET 2 NOVEMBER 19, 2024 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
If (a,b,c) means (a – b) × (a – c) × (b + c), find (5, 2, 3) in simplest form.
1) __________
2)
Express 0.375 as a fraction in lowest terms.
2) __________
3)
If 4x = 64, express 2x+1 in terms of powers of 2.
3) __________
4)
A positive number equals three-fourths of the sum of the number and its reciprocal. Find the number.
4) __________
5)
Triangle PQR ~ Triangle STU. If PQ = 6, QR = 8, and ST = 9, find TU.
5) __________
6)
How many 3-inch squares can be cut from a 15-inch by 12-inch rectangle?
6) __________
CML SAMPLE
TEST 7
NAME _________________________________ GRADE 7
EUCLIDEAN DIVISION MEET 5 FEBRUARY 11, 2025 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
What is the greatest 3-digit number that is divisible by both 4 and 9?
1) __________
2)
If 3x – 7 = 2x + 5, find the value of x + 3.
2) __________
3)
The area of a square is 81 square feet. What is the perimeter of the square?
3) __________
4)
A bag contains 5 red marbles and 3 blue marbles. If two marbles are drawn without replacement, what is the probability both are red?
4) __________
5)
Find the least common multiple of 12, 15, and 18.
5) __________
6)
A rectangular garden is 3 times as long as it is wide. If the perimeter is 48 meters, what is the area?
6) __________
CML SAMPLE
TEST 8
NAME _________________________________ GRADE 8
PYTHAGOREAN DIVISION MEET 3 DECEMBER 17, 2024 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
Evaluate: (23 + 32) ÷ (4 – 1) + 5 × 2
1) __________
2)
If the pattern continues: 2, 6, 18, 54, …, what is the 7th term?
2) __________
3)
A cylinder has radius 4 cm and height 10 cm. What is its volume? (Use π = 3.14)
3) __________
4)
In a class of 30 students, 18 play soccer and 15 play basketball. If 8 students play both sports, how many play neither?
4) __________
5)
Solve for y: 2y – 34 = y + 13
5) __________
6)
The diagonals of a rhombus are 16 cm and 12 cm. What is the area of the rhombus?
6) __________
CML SAMPLE
TEST 9
NAME _________________________________ GRADE 9
EUCLIDEAN DIVISION MEET 3 DECEMBER 14, 2024 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
Solve for x: log3(x+2) – log3(x-1) = 1
1) __________
2)
The sum of the first n positive integers is n(n+1)2. Find the sum of integers from 1 to 100.
2) __________
3)
If the quadratic equation x2 + bx + c = 0 has roots 3 and -5, find the value of b + c.
3) __________
4)
The point (4, -3) is rotated 90° clockwise around the origin. What are the coordinates of the resulting point?
4) __________
5)
Factor completely: x4 – 16
5) __________
6)
In a right triangle, one leg is 5 units long, and the hypotenuse is 13 units long. What is the length of the other leg?
6) __________
CML SAMPLE
TEST 10
NAME _________________________________ GRADE 9
PYTHAGOREAN DIVISION MEET 4 JANUARY 21, 2025 30 MINUTES
ANSWER COLUMN
Directions: Place your answer to each question below in the answer column.
1)
Simplify: 2x3y2z4xy4z2
1) __________
2)
A coin is flipped 8 times. What is the probability of getting exactly 5 heads?
2) __________
3)
Solve the system of equations: 3x + 2y = 14 and 5x – 3y = 1. Give your answer as an ordered pair (x, y).
3) __________
4)
In triangle ABC, angles A, B, and C are in the ratio 2:3:4. What is the measure of the largest angle in degrees?
4) __________
5)
If f(x) = x2 – 3x + 2 and g(x) = 2x + 1, find f(g(3)).
5) __________
6)
The sequence an is defined by a1 = 4 and an+1 = 2an – 1 for n ≥ 1. Find the value of a5.
6) __________